Question

1. You are saving to buy a new house in 7 years. If you invest $4,500 now at 5.5% interest compounded

quarterly, how much money will you have to use for your down payment?

2. You have your heart set on buying a new car in 2 years. You invest $3,200 at 3.75% interest
compounded continuously. How much money will have to use for your down payment on your new
car?

3. You are a proud new parent of a baby girl. In eighteen years, you will want to help her pay for college.
How much do you need to invest now at 4.75% interest compounded monthly so you can help her pay
for the $40,000 expense of college?

4. After building your new home, you decide you would like to install an in-ground pool in 7 years. How
much do you need to invest now at 5.25% interest compounded continuously to have the $30,000 you
will need to build the pool?

5. You recently received an inheritance of $11,500 from your grandparents. Which option is the best way
to invest your money and how much better is the best investment? Option A: 5.6% interest
compounded semi-annually for 8 years or Option B: 3.45% interest compounded continuously for 5
years.
Part A)
Part B)
Part C)

Answer 1

Explanation:

Q1.

Use FV formula to get value at year 7

FV= PV
`(1+r)^(t)`

Since it's quarterly compounding, quarterly rate would be (5.5% / 4)= 1.375% and total duration t would be 7*4 = 28 quarters

FV= 4,500
`(1+0.01375)^(28)  = 4,500 * 1.46576478`

FV= $6,595.94

Q2.

Future Value with continuous compounding formula; FV= PV
`e^(rt)`

Note: the "e" is an exponential

FV= 3,200
`e^(0.0375 * 2)`

FV = 3200* 1.0778841

FV= $3,440.229

Q3.

Here, you find Present value; PV =
`(FV)/((1+r)^(t) )`

Since it's monthly compounding, monthly rate would be (4.75% / 12)= 0.3958% and total duration t would be 18*12 = 216 months

PV=
`(40,000)/((1+0.003958)^(216) )`

PV= 40,000/2.3472409

PV= 17,041.2845

Therefore you need to invest $17,041.28.

Q4.

Use PV with continuous compounding formula here;

PV=
`(FV)/(e^(rt) )`

Note: the "e" is an exponential

PV =
`(30,000)/(e^(0.0525 * 7) ) \\`

PV= 30,000/1.4441198

PV = $20,773.8998

Therefore, you need to invest $20,773.90 now.

Q5.

Compare the FV of each option and choose the highest;

a.) FV= PV
`(1+r)^(t)`

Since it's semi-annual compounding, semi-annual rate would be (5.6% / 2)= 2.8% and total duration t would be 8*2 = 16

FV = 11,500
`(1+0.028)^(16)  = 11,500 * 1.555570987`

FV= $17,889.07

b.)Future Value with continuous compounding formula; FV= PV
`e^(rt)`

Note: the "e" is an exponential

FV= 11,500
`e^(0.0345 * 5)`

FV= 11,500 * 1.188271821

FV= $13,665.126

Therefore, Option A is a better option by $4,223.94